Sin4x-sinx=0 Найти кони ** промежутке

Question

Sin4x-sinx=0
Найти кони на промежутке

Answer 1

2sin(3x/2)cos(5x/2)=0
sin(3x/2)=0
3x/2=πk
x=2πk/3,k∈z
π≤2πk/3≤5π/2
6≤4k≤15
6/4≤k≤15/4
k=2  x=4π/3
k=3  x=2π
cos(5x/2)=0
5x/2=π/2+πk
x=π/5+2πk/5
π≤π/5+2πk/5≤5π/2
10≤2+4k≤25
8≤4k≤23
2≤k≤23/4
k=2  x=π
k=3  x=7π/5
k=4  x=9π/5
k=5  x=11π/5